multiply and simplify by factoring. Assume that all expressions under radicals represnt nonegative numbers.
3�ãy^4 3�ã81^3
What radicals? Need to repost in clearer terms.
I tried using the symbol but it will does not recognize it here. It's the check mark with a horizontal line.
3^symbol over y^4 3^symbol over 81y^3
still not totally clear.
is it 3√(y^4)*(3√ 81)y^3 or
is it 3√(y^4)*3√(81y^3) ?
(on a PC, I get the √ sign by holding down the Alt key then typing 251 on the number pad, then releasing the Alt key)
3�ã(y^4)*3�ã(81y^3)
This one.
Thanks!
To multiply and simplify by factoring, we can rewrite the given expression using the product of square roots property:
√(a) * √(b) = √(a * b)
Applying this property to √(y^4) and √(81^3), the expression becomes:
√(y^4) * √(81^3) = √(y^4 * 81^3)
Next, let's simplify each term separately:
√(y^4) = y^2
To simplify √(81^3), we need to factor it. Since 81 is a perfect square, we can express it as (9^2):
√(81^3) = √((9^2)^3)
Using the power property of radicals, we can rewrite this as:
= √(9^(2*3))
= √(9^6)
Simplifying further, we have:
= 9^3
Putting it all together, we get:
√(y^4 * 81^3) = y^2 * 9^3
So, the simplified expression is y^2 * 9^3.