Question

Q) Write in Index form:
'Square root of fifth index of 121.'
Ans. ?

Answer 1

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Answer 2

The index form of the given expression is $(11)^{5}$

Step-by-step explanation:

The given expression is

$\sqrt{(121)^{5}}$

We can write 121 as 121 = 11². So, the expression becomes

$\sqrt{(11^2)^{5}}$

Now, use the exponent property: $(x^m)^n=x^{mn}$

$\sqrt{(11)^{10}}$

Finally, use the property: $\sqrt[n]{x}=x^n$

$(11)^{10\cdot\frac{1}{2}}$

This can be further simplified as

$(11)^{5}$

Therefore, the index form of the given expression is $(11)^{5}$

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