Division of Numbers with Square Roots

Q.

If $x=2\sqrt{2}+\sqrt{7}$, identify the value of $\frac{1}{2}(x+\frac{1}{x})$.

1. $2\sqrt{2}-\sqrt{7}$

2. $\sqrt{7}$

3. $2\sqrt{2}$

4. $2\sqrt{2}+\sqrt{7}$

Q.

If a and b are rational numbers and $\frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}=a-b\sqrt{77},$ find the values of a and b.

1. $a=\frac{9}{2}andb=\frac{4}{3}$

2. $a=\frac{1}{2}andb=\frac{1}{2}$

3. $a=\frac{9}{2}andb=\frac{1}{2}$

4. $a=\frac{1}{3}andb=\frac{9}{2}$

Q.

$-\frac{\sqrt{28}}{\sqrt{343}}$ is a/an ________ .

1. fraction

2. natural number

3. irrational number

4. rational number

Q.

$\frac{\sqrt{32}+\sqrt{48}}{(\sqrt{8}+\sqrt{12})}=?$

1. $\sqrt{2}$

2. $2$

3. $8$

4. $4$

Q.

Simplify the ratio $\sqrt{36}:\sqrt{9}$

1. 3:1

2. 4:1

3. 2:1

4. 2:3

Q.

Question 1 (ii)
Classify $(3+\sqrt{23})-\sqrt{23}$ as rational or irrational.

Q.

Question 9 (ii)
Classify $\sqrt{225}$ as rational or irrational.

Q.

Question 1 (iii)
Classify $\frac{2\sqrt{7}}{7\sqrt{7}}$ as rational or irrational.

Q.

Express each one of the following with rational denominator:

$\frac{14}{\sqrt{98}}$

Q. In the following equations find which variables x, y, z, etc., represent rational or irrational
numbers.
(iv) $u^2=\frac{17}{4}$

Q.

In a ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ triangle, the length of the hypotenuse is $9\sqrt{2}$. What is the length of its sides?

1. $8units$

2. $6units$

3. $9units$

4. $7units$

Q. Show that $\sqrt[3]{36}$ is not a rational number.

Q. On simplifying, the ratio $\sqrt{36}:\sqrt{9}$ equals .

1. 2:1
2. 3:1
3. 4:1

Q. If $p$ and $q$ are rational numbers, then find $p$ and $q$ given that $\frac{4+\sqrt{14}}{4-\sqrt{14}}=p+q\sqrt{14}$

1. $p=15,q=4$
2. $p=-15,q=4$
3. $p=15,q=-4$
4. $p=-15,q=-4$

Q.

Find the quotient when $8\sqrt{3}$ is divided by $\sqrt{1}2$.

1. $2\sqrt{3}$

2. 4

3. $4\sqrt{2}$

4. $\sqrt{14}$

Q. Question 15
The value of $\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}$ is

A) $\sqrt{2}$
B) 2
C) 4
D) 8

Q. Simplify the ratio $\sqrt{36}:\sqrt{9}$

Q. Given, find the value of a, if $[3–\sqrt{5}]/[3+2\sqrt{5}]=-19/11+a\sqrt{5}$

Q. $20:\sqrt{2}$ can be simply written as $10:\sqrt{1}$.

1. False
2. True

Q. Simplify this$\frac{\sqrt{28}}{\sqrt{343}}$ , and find the type of number obtained.

1. real number
2. None of the above
3. rational number
4. irrational number

Q. Compare the following pair of ratio.
$\frac{\sqrt{5}}{3},\frac{3}{\sqrt{7}}$

Q.

Rationalising $\frac{\sqrt{2}+\sqrt{3}}{\sqrt{3}-\sqrt{2}}$ will give __________.

1. $5-2\sqrt{6}$

2. $5+2\sqrt{6}$

3. $7+2\sqrt{6}$

4. $7-2\sqrt{6}$

Q.

0.12333... can be expressed in rational form as

1. $\frac{900}{111}$

2. $\frac{111}{900}$

3. $\frac{123}{10}$

4. $\frac{121}{900}$