# Tamilnadu Board Class 9 Maths Solutions Chapter 2 Real Numbers Ex 2.5

## Tamilnadu State Board Class 9 Maths Solutions Chapter 2 Real Numbers Ex 2.5

Question 1.
Write the following in the form of 5n:
(i) 625
(ii) $$\frac { 1 }{ 5 }$$
(iii) √5
(iv) $$\sqrt { 125 }$$
Solution:
(i) 625 = 54

(ii) $$\frac { 1 }{ 5 }$$ = 5-1

(iii) √5 = 5$$\frac { 1 }{ 2 }$$

(iv) $$\sqrt { 125 }$$
$$=\sqrt{5^{3}}=\left(5^{3}\right)^{\frac{1}{2}}=5^{\frac{3}{2}}$$

Question 2.
Write the following in the form of 4n:
(i) 16
(ii) 8
(iii) 32
Solution:
(i) 16 = 42
(ii) 8 = $$4^{1} \times 4^{\frac{1}{2}}=4^{1+\frac{1}{2}}=4^{\frac{3}{2}}$$
(iii) 32 = $$4 \times 4 \times 4^{\frac{1}{2}}=4^{2+\frac{1}{2}}=4^{\frac{5}{2}}$$

Question 3.
Find the value of
(i) (49)$$\frac { 1 }{ 2 }$$
(ii) (243)$$\frac { 2 }{ 5 }$$
(iii) 9$$\frac { -3 }{ 2 }$$
(iv) ($$\frac { 64 }{ 125 }$$)$$\frac { -2 }{ 3 }$$
Solution:

Question 4.
Use a fractional index to write:
(i) √5
(ii) $$\sqrt[2]{7}$$
(iii) ($$\sqrt[3]{49}$$)5
((iv) $$\left(\frac{1}{\sqrt[3]{100}}\right)^{7}$$
Solution:

Question 5.
Find the 5th root of
(i) 32
(ii) 243
(iii) 100000
(iv) $$\sqrt[1024]{3125}$$
Solution: