Question

Whole root of √x√x√x=6 find the value of x

Answer 1

Question:

Find x, $\sqrt{x\sqrt{x\sqrt{x}}}=6$

Solution:

Given, $\sqrt{x\sqrt{x\sqrt{x}}}=6$

Squaring both sides, we get

$(\sqrt{x\sqrt{x\sqrt{x}}})^{2}=6^{2}$

or, $x\sqrt{x\sqrt{x}}=6^{2}$

Again, squaring both sides, we get

$(x\sqrt{x\sqrt{x}})^{2}=6^{4}$

or, $x^{2}\times x\sqrt{x}=6^{4}$

or, $x^{3}\sqrt{x}=6^{4}$

Again, squaring both sides, we get

$(x^{3}\sqrt{x})^{2}=6^{8}$

or, $x^{6}\times x=6^{8}$

or, $x^{7}=6^{8}$

or, $x=\sqrt[7]{6^{8}}$

or, $x=\sqrt[7]{1679616}$

Therefore, the required solution is

$x=\sqrt[7]{1679616}$