how do i solve 3√8x^2y^3 - 5x√32y^3
or
4√98y^11 - 9√128y^11
solve? There is no equal sign in the phrase.
yea im supposed to subtract them. all the directions say is to subtract.
Ok, I can't decide what you wanted under the sqrt sign. I think you meant this:
3sqrt(8x^2y^3) - 5xsqrt(32y^3)
so work on the sqrt sign first
3sqrt(4*2x^2y^3)- 5xsqrt(16*2y^3)
6sqrt( 2x^2y^3) - 20xsqrt( 2y^3)
6xsqrt( 2 y^3) - 20xsqrt( 2y^3)
or
sqrt(2y^3)(6x-20x)
-14x sqrt(2y^3)
To solve expressions involving square roots and variables, you need to simplify the expressions by factoring out perfect squares. Let's break down the steps for each expression.
Expression 1: 3√8x^2y^3 - 5x√32y^3
Step 1: Simplify the terms under each square root:
√8 = √(4 * 2) = 2√2
√32 = √(16 * 2) = 4√2
Expression becomes: 3 * 2√2 * x^2 * y^3 - 5x * 4√2 * y^3
Step 2: Combine like terms:
6√2 * x^2 * y^3 - 20√2 * x * y^3
Expression 2: 4√98y^11 - 9√128y^11
Step 1: Simplify the terms under each square root:
√98 = √(49 * 2) = 7√2
√128 = √(64 * 2) = 8√2
Expression becomes: 4 * 7√2 * y^11 - 9 * 8√2 * y^11
Step 2: Combine like terms:
28√2 * y^11 - 72√2 * y^11
In both expressions, the common factor is √2, so we can factor it out:
Expression 1: 2√2 * (3x^2 * y^3 - 10x * y^3)
Expression 2: 4√2 * (7y^11 - 18y^11)
Simplifying further:
Expression 1: 6√2 * (x^2 * y^3 - 5x * y^3)
Expression 2: 28√2 * (-11y^11)
Therefore, the simplified expressions are:
Expression 1: 6√2xy^3 * (x - 5)
Expression 2: -308√2y^11
Note that we factored out a common factor of y^11 in Expression 2.