What is the answer to (xsqrt(x))^2=64 ?

The answer to (xsqrt(x))^2=64 is x=4

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(xsqrt(x))^2=64

(x x)^{2} = 64

x = 4

Solution steps

(x x)^{2} = 64

Move

64

to the left side

(x)^{2} x^{2} - 64 = 0

Factor

(x)^{2} x^{2} - 64 : (x x + 8) (x x - 8)

(x x + 8) (x x - 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x x + 8 = 0 or x x - 8 = 0

Solve

x x + 8 = 0 :

No Solution for

x \in R

Solve

x x - 8 = 0 : x = 4

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

(x + 5) (x^{2} + 1) = 0

5 x - 4 - x = 0

- 4 = - 6 + 2 x

7 x + 92 = 3 x + 20

3 - x + 7 = 2