# CBSE Class 9  Maths - Number Systems - Very Short Answer Based Questions

Q1: Simplify $\sqrt[4]{32}$ ?

$\sqrt[4]{32} = \left ( 32 \right )^{\frac{1}{4}}$

$= \left ( 2^5 \right )^{\frac{1}{4}}$

$= \left ( 2^4 . 2^1 \right )^{\frac{1}{4}}$

$= \left ( 2^4 \right )^{\frac{1}{4}}.(2)^{\frac{1}{4}}$

$= 2.\sqrt[4]{2}$

Q2:  Simplify $\sqrt{8} + \sqrt{32} - \sqrt{2}$

$= \sqrt{8} + \sqrt{32} - \sqrt{2}$

$= \sqrt{4\times 2} + \sqrt{16 \times 2} - \sqrt{2}$
$= 2\sqrt{2} + 4\sqrt{2} - \sqrt{2}$
$= 5\sqrt{2}$

Q3: All natural numbers together with zero i.e. 0, 1, 2, 3, 4, ..... are known as _______ numbers. (Fill in the blank.)

Q4: Simplify $\left ( \sqrt{5} + \sqrt{3} \right )^2$.

$= \left ( \sqrt{5} + \sqrt{3} \right )^2$
$= \left ( \sqrt{5} \right )^2 + \left ( \sqrt{3} \right )^2 + 2\left ( \sqrt{5} \right )\left (\sqrt{3} \right )$
$= 5 + 3 + 2\left ( \sqrt{15} \right )$
$= 8 + 2\sqrt{15}$

Q5: Every point on the number line represents a unique ________ number. (Fill in the blank)

Q6: What is the product of $\left ( 8 + 3\sqrt{2} \right )\left ( 8 - 3\sqrt{2} \right )$?

$=\left ( 8 + 3\sqrt{2} \right )\left ( 8 - 3\sqrt{2} \right )$
$=\left ( 8 \right )^2 - \left (3\sqrt{2} \right )^2$
$=64 - \left ( 9 \times 2 \right )$
$= 64 - 18$
= 46

Q7: The sum or difference of a rational number and an irrational number is________. (Fill in the blank)