Answer:
2x²√13
Step-by-step explanation:
Step 1: When there is multiplication under a square root sign (also called a radical sign), you can rewrite the expression as the product of two square roots, like this...
√(52x^4) can be rewritten as (√52)(√x^4)
Step 2: x^4 = x²x², so it's the same thing as saying (x²)², or "x-squared, squared". Taking the square root of it leaves just x-squared, so this simplifies to
(√52)x²
Step 3: When taking the square root of a number that is not a perfect square, you need to do a factor tree to see if you can break the number up into a product of perfect squares, or a perfect square multiplied by a prime number.
52 is an even number, so we an at least divide by 2.
52/2 is 26, so we have
(26)(2)
2 is a prime number, so we don't break that down any further.
26 is even so it is also divisible by 2,
26/2 is 13, so we have
(13)(2)(2)
which we can write as (13)(4) (groups pairs of numbers together)
(2)(2) is 4, which results in a perfect square, so we can rewrite √52 as
(√4)(√13), since √4 = 2, we simplify this expression to
2√13
So √(52x^4) breaks down to (√52)(√x^4), which further breaks down into
(2√13)(x²)
We simplify the expression to 2x²√13
