Question

What is the simplest form of square root of

Answer 1

First you simplify the fraction and variables inside the root. Reduce 126/32 and use exponent rules for dividing variables(subtract the exponents). This will give you,
$\sqrt{ \frac{63 {y}^{5} }{16 {x}^{2} } }$
Then move onto the root. Using radical properties you take the root of the numerator and denominator seperately. Since the root of the numerator is not a rational number or perfect square it stays as,
$\sqrt{63 {y}^{5} }$
Altogether the new equation will be this,
$\frac{ \sqrt{63 {y}^{5} } }{4x}$
You can still simplify this further by reducing the radical in the numerator.
You prime factor it to give you 7×9 = 63 which lets you factor out a 3. You can also factor out 4 of the y variables. Breaking down the numerator you get this.
$\sqrt{ {3}^{2} } \sqrt{ {y}^{4} } \sqrt{7y}$
Which simplifies to,
$3 {y}^{2} \sqrt{7y}$
Your final simplest form equation is,
$\frac{3 {y}^{2} \sqrt{7y} }{4x}$