Question

I need help on this!

Answer 1

Let us solve the given equations.

Consider the equation 1,

$x^2 = 49$

$x = \sqrt{49}$

So, x = 7 and -7

Consider the equation 2,

$x^3 = 27$

$x = (27)^ \frac{1}{3}$

$x = (3^3)^ \frac{1}{3}$

$x = 3$

Consider the equation 3,

$x^2 = 24$

$x = \sqrt{24}$

$x = \sqrt{2 \times 2 \times 2 \times 3}$

$x = 2 \sqrt{6}$

Consider the equation 4,

$x^3 = -71$

$x = (-71)^ \frac{1}{3}$

$x = (-1)^\frac{1}{3} (71)^\frac{1}{3}$

So, $x = (-1^3)^\frac{1}{3} (71)^\frac{1}{3}$

$x = - (71)^\frac{1}{3}$

Consider the equation 5,

$x^2 = -25$

$x = \sqrt{-25}$

So, x = 5i and -5i

Consider the equation 6,

$x^2 = 85$

$x =\sqrt{85}$

$x = \sqrt{5 \times 17}$

Since, both are prime numbers.

So, $x =\sqrt{85}$