Question

what will be the value of the given no. How to find it with simple method.

Answer 1

Hey it is very simple....
Let us assume that..

x=414x=414

⇒x4=4⇒x4=4

⇒x4–(2–√)4=0⇒x4–(2)4=0

⇒[x2+(2–√)2][x2−(2–√)2]=0⇒[x2+(2)2][x2−(2)2]=0

⇒x2−(2–√)2=0⇒x2−(2)2=0

⇒[x+2–√][x−2–√]=0⇒[x+2][x−2]=0

⇒x−2–√=0⇒x=2–√⇒x−2=0⇒x=2

Or x=−2–√x=−2

And x2+(2–√)2=0x2+(2)2=0

⇒x=±i2–√⇒x=±i2

Hence the required fourth roots of 44 are ±2–√,±i2–√±2,±i2

Problem is done.

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Answer 2

$\sqrt[4]{4} = {4}^{ \frac{1}{4} } = {2}^{ \frac{1}{2} } = \sqrt{2} = 1.414$