Simplify the radical expression
square root 48a squared b to the 7th all beneath the sq rt sign I have no work to show, can't remember the steps to solve
√(48a^2b^7)
recall that √x^2 = x, so factor out all the perfect squares:
√(16*3*a^2*b^6*b)
√(16a^2b^6)√(3b)
4ab^3 √3b
My problem is 48 a^ b to the 7th power all under the sq rt sign (don't know how to make the sign on my computer) I wasn't very clear before. Steve or anyone could you walk me through this...math (especially) algebra is NOT my forte'
To simplify the given radical expression, we need to break down the expression into its factors and simplify each individual square root.
Let's start by writing the expression with its prime factorization:
√(48a^2b^7)
First, let's simplify the square root of the numbers under the radical sign:
√(48) = √(16 × 3) = √(4 × 4 × 3) = 4√3
Now, let's simplify the square root of the variables:
√(a^2b^7) = √(a^2) × √(b^7) = a√(b^6 × b) = a√(b^6) × √(b) = a × b^3√(b)
Putting it all together, we have:
√(48a^2b^7) = 4a × b^3√(3)
Therefore, the simplified radical expression is 4ab^3√3.