Question

Can some one help me please

Answer 1

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