Question

Based on this information answer the questions given below.
(i) $\sqrt[m]{m{a}^x\sqrt[m]{m{a}^x\sqrt[m]{m{a}^x\sqrt[m]{m{a}^x}}}}$ and so on, for k times,i.e., number of radical signs $=k$
$\sqrt[m^k]{m^k{a}^{x(m^k-1)}}\therefore$ Resulting index $=mxmx.......k$times
$=a^{\frac{x(m^k-1)}{m^k}}=m^k$
(ii) $\sqrt{p\sqrt{p\sqrt{p}}}$ to infinity $=p$ always where p is any number. Find the value of $\sqrt{100\sqrt{100\sqrt{100}}}$ to infinity.

• A. 10
• B. 100
• C. ${100}^3$
• D. $\sqrt{{10}^3}$

Answer 1

The correct option is B 100

$Letx=\sqrt{100\sqrt{100\sqrt{100}........}}then{x}^2=100\sqrt{100\sqrt{100\sqrt{100}........}}{x}^2=100xx(x-100)=0x=0orx=100$

So correct answer from the option will be option B