Choose the Correct options
0 of 37 Questions completed
Questions:
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 37 Questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Average score 

Your score 

Are there two irrational number whose sum and product both are rationals ? Justify
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Yes, and are two irrational numbers
Sum
Product
Prove that the negative of an irrational number is an irrational number.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let negative of an irrational number be rational number
Let P be an irrational number by the assumption P is a rational number. Since negative of a rational number is rational (P) = P is a rational number but we assumed P as an irrational number. So our assumption is wrong, so negative of an irrational number is irrational.
Find 4 rational numbers between \(\dfrac{1}{3} \) and \(\dfrac{4}{5} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
are 4 rational numbers
Express \(1.\bar{323} \) in the form \(\dfrac{p}{q} \), where \(p \) and \(q \) are integers \(q\ne0 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let
Simplify : \(\left(\dfrac{81}{16}\right)^{\frac{3}{4}}\times\left\{\left(\dfrac{25}{9}\right)^{\frac{3}{2}}\div\left(\dfrac{5}{2}\right)^{3}\right\} \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Show that \(\dfrac{x^{a(bc)}}{x^{b(ac)}}\div\left(\dfrac{x^b}{x^a}\right)^c=1 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Locate \(\sqrt{13} \) on the number line.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Represent \(\sqrt{5.6} \) on the number line.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Presentation of on number line:
Mark the distance 5.6 units from a fixed points A on a given line to obtain a point B such that AB=5.6 units. From B, mark a distance of 1 unit and mark the new points as C. Find the midpoint of AC and mark the points as O. Draw a semicircle with centre O and radius OC. Draw a line perpendicular to AC passing through B and intersecting the semicircle at D. Then .
Now, draw an arc with centre B and radius BD, which intersects the number line in E.
Thus, E represent
If \(a+b\sqrt3=\dfrac{\sqrt31}{\sqrt3+1} \), find the values of \(a \) and \(b \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Express \(\dfrac{y^2}{\sqrt{x^2+y^2}+x} \) with rational denominator
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Find the values of \(x \) and \(y \) if \(\mathrm{(A)\ \dfrac{7+\sqrt5}{7\sqrt5}}\dfrac{7\sqrt5}{7+\sqrt5}=x+\dfrac{7}{11}\sqrt5y \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(x=\dfrac{\sqrt31}{\sqrt3+1} \) and \(y=\dfrac{3+2\sqrt2}{32\sqrt2} \) then find the value of \( x+y\).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Express \(3.42\bar5 \) in the form \(\dfrac{p}{q} \), where \(p \) and \(q \) are integers, \(q\ne0 \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(\dfrac{\sqrt31}{\sqrt3+1}=a+b\sqrt3 \). find the values of a and b.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(a=\dfrac{3\sqrt5}{3+\sqrt5} \) and \(b=\dfrac{3+\sqrt5}{3\sqrt5} \), find \( a^2b^2\).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(\dfrac{\sqrt2\sqrt5}{\sqrt2+\sqrt5}=a+b\sqrt{10} \), find the values of a and b.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(\dfrac{3+\sqrt7}{3\sqrt7}+\dfrac{3\sqrt7}{3+\sqrt7}=a+b\sqrt7 \), find the values of a and b.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Find the value of \(a \), if \(\dfrac{3\sqrt5}{3+2\sqrt5}=a\sqrt5\dfrac{19}{11} \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(x=2+\sqrt5 \) find the value of \(\left(x^2\dfrac{1}{x^2}\right) \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(x=\dfrac{\sqrt5\sqrt2}{\sqrt5+\sqrt2} \) and \(y=\dfrac{\sqrt5+\sqrt2}{\sqrt5\sqrt2} \), find the value of \(x^2+xy+y^2 \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Simplify : \(\dfrac{\sqrt6}{\sqrt2+\sqrt3}+\dfrac{3\sqrt2}{\sqrt6+\sqrt3}\dfrac{4\sqrt3}{\sqrt6+\sqrt2} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Express \(\dfrac{3}{\sqrt3\sqrt2+\sqrt5} \) with rational denominator
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(x=7+4\sqrt3 \) find the value of \(\left(x^3+\dfrac{1}{x^3}\right) \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(x=\dfrac{\sqrt3+\sqrt2}{\sqrt3\sqrt2} \) and \(y=\dfrac{\sqrt3\sqrt2}{\sqrt3+\sqrt2} \), then find the value of \(x^2+y^210xy \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Find the square root of 4.2 geometrically.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Draw AC = 4.2
Take mid point as O
now draw a circle of OA = OC radius from centre O
Now take a point B from O at OB distance and make perpendicular D
Now BD is measure it
Show that \(\dfrac{1}{1+\sqrt2}+\dfrac{1}{\sqrt2+\sqrt3}=1+\sqrt3 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(x=3+2\sqrt2 \), find the value of \(\left(\sqrt x\dfrac{1}{\sqrt x}\right) \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Find the square root of 4.5 geometrically.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Step 1: Draw a number line. Mark O as the zero on the number line.
Step 2: Mark a point A as 4.5 on the number line.
Step 3: Mark a point C as 1 on the number line.
Step 4: Mark a point B as the midpoint of AC.
Step 5: With point B as the centre and radius as AB draw a semicircle.
Step 6: From O draw a perpendicular line to the number line that intersects the previous drawn semicircle at D. Here OD = square root of 4.5.
Step 7: With O as centre and radius as OD, draw an arc that intersects the number line at point E. Here E is the point square root of 4.5 on the number line.
If \(a = 2, b = 3\), then find the values of the following
(A) \((a^b+b^a)^{1} \) (B) \((a^a+b^b)^{1} \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Prove that \(\dfrac{1}{1+x^{ab}}+\dfrac{1}{1+x^{ba}} =1\).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Express \(2.02\bar5 \) in the form of \(\dfrac{p}{q} \), where \(p \) and \(q \) are integers and \(q\ne0 \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Express \(0.6+0.\bar 7+0.4\bar7 \) in the form \(\dfrac{p}{q} \), where \(p,q\in Z,q\ne0 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let
Required sum
If \(a=5+2\sqrt6 \) and \(b=\dfrac{1}{a} \), then find the value of \(a^2+b^2 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Find the value of : \(\dfrac{1}{1+\sqrt2}+\dfrac{1}{\sqrt2+\sqrt3}+\dfrac{1}{\sqrt3+\sqrt4}+…..\dfrac{1}{\sqrt8+\sqrt9} \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Find the values of \(a \) and \(b \) if : \(\dfrac{7+3\sqrt5}{3+\sqrt5}\dfrac{73\sqrt5}{3\sqrt5}=a+\sqrt{5b} \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(a=74\sqrt3 \), find the value of \(\left(\sqrt a+\dfrac{1}{\sqrt a}\right) \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Represent \(\sqrt{9.3} \) on the number line.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Steps:
1) Draw a line segment AB of length 9.3 units.
2) Extend the line by 1 unit more such that BC=1 unit .
3) Find the midpoint of AC.
4) Draw a line BD perpendicular to AB and let it intersect the semicircle at point D.
5) Draw an arc DE such that BE = BD.
Therefore, BE = units