Question

If x^1/8 = m and x,^1/4 = n and n = 4 m then find the value of rootx
(A) 512
(B) 216
(C) 324
(D) 256
(E) None of these​

Answer 1

Answer:

(B)256

Explanation:

$\sqrt[1 \div 8]{x } = \sqrt[1 \div 4]{x} \times \sqrt[]{x}$

$\sqrt[1 \div 8]{x } = x \: to \: the \: power \:( 1 \div 4 \:) \times( 1 \div 2)$

$m = n \: to \: the \: power \: 1 \div 2$

$m = \sqrt[]{n}$

$m = \sqrt{4m}$

${m}^{2} = 4m$

${m}^{2} - 4m = 0$

m(m-4)=0

m-4=0

so, m=4

Now

x^1/8=4

x ^{(1/8)×4}=4^4

x^1/2=256

Therefore the correct option is B)256

Answer 2

Answer:



Step-by-step explanation

x⅛=m,x¼=

n=4m

x¼=4(x⅛)

bracket raised to 4 on both sides

(x¼)⁴=4⁴(x⅛)

x=256x½

x/x½=256

x½=256

√x=256