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 5^th root of
(i) 32
(ii) 243
(iii) 100000
(iv) \(\sqrt[1024]{3125}\)
Solution:

Samacheer Kalvi 9th Maths Book Answers