Samacheer Kalvi 9th Maths Solutions Chapter 2 Real Numbers Ex 2.5

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Tamilnadu Samacheer Kalvi 9th 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) \(\sqrt { 5 }\)
(iv) \(\sqrt { 125 }\)
Solution:
(i) 625 = 5⁴

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

(iii) \(\sqrt { 5 }\) = 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

Solution:

Question 4.
Use a fractional index to write:
(i) \(\sqrt { 5 }\)
(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) \(\frac{1024}{3125}\)
Solution: