Answer:2x²√13Step-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)x²Step 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√13So √(52x^4) breaks down to (√52)(√x^4), which further breaks down into (2√13)(x²)We simplify the expression to 2x²√13