√(21x^2y/(75xy^5)
it says on my paper to enter it: √b, enter sqrt(b). For example: For 4√3 enter 4sqrt(3)
Please help, I've got 5 wrong! :(
If �ã(21x^2y/(75xy^5) mean:
sqrt ( 21 * x^2 * y / ( 75 * x * y^5))
then:
sqrt ( 21 * x^2 * y / ( 75 * x * y^5) ) =
sqrt ( 3 * 7 * x^2 * y / ( 3 * 25 * x * y^5 ) ) =
sqrt ( 7 * x / ( 25 * y^4 ) ) =
sqrt ( 7 x ) / sqrt ( 25 y^4) =
sqrt ( 7 x ) / 5 y^2
To simplify the given expression √(21x^2y/(75xy^5), you can follow these steps:
Step 1: Break down the expression into its components.
The given expression can be broken down into:
√(21x^2y) / √(75xy^5)
Step 2: Simplify each component.
For the numerator (√(21x^2y)), you can simplify the square root by breaking it down into the product of square roots:
√(21x^2y) = √21 * √(x^2) * √y
Since x^2 is a perfect square, √(x^2) simplifies to x. We also know that √21 and √y cannot be simplified any further.
For the denominator (√(75xy^5)), we can apply the same process:
√(75xy^5) = √(25 * 3 * x * y^4) = √25 * √(3 * x * y^4)
Just like before, √25 simplifies to 5, and √(3 * x * y^4) cannot be simplified further.
Step 3: Put the simplified components together.
Now, you have:
(√21 * x * √y) / (5 * √(3 * x * y^4))
Step 4: Combine like terms.
To simplify further, you can cancel out common factors between the numerator and denominator. In this case, the common factors are x and y.
(√21 * x * √y) / (5 * √(3 * x * y^4))
= (√21 * √y) / (5 * √(3 * y^4))
= (√21 * √y) / (5 * y^2)
Step 5: Rewrite the expression in the required format.
To follow the given format, √b, rewrite the expression as:
(1/(5 * y^2)) * √(21y)
So, the simplified form of √(21x^2y/(75xy^5)) is (1/(5 * y^2)) * √(21y).