Square root of 14abc times the square root of 2ab
note that we can rewrite the squareroot of a number by raising this number by 1/2
example, sqrt(5) = 5^(1/2)
therefore in the problem we have
sqrt(14abc) = (14abc)^(1/2) = [14^(1/2)][a^(1/2)][b^(1/2)][c^(1/2)]
sqrt(2ab) = (2ab)^(1/2) = [2^(1/2)][a^1/2][b^1/2]
now for the variables of the same base, we just add the exponents, and for constants we multiply the base and retain the exponent:
14^(1/2) * 2^(1/2) * a^(1/2 + 1/2) * b^(1/2 + 1/2) * c^(1/2)
28^(1/2) * a*b*c^(1/2)
2*sqrt(7) * ab* sqrt(c)
hope this helps~ :)
Thank you
To find the square root of 14abc times the square root of 2ab, you can use the properties of square roots.
First, let's break down the expression:
√(14abc) * √(2ab)
We can combine these square roots using the product property of square roots, which states that the square root of a product is equal to the product of the square roots:
√(14abc * 2ab)
Next, we can simplify the expression under the square root:
√(28a²bc²)
Now, let's break down this expression further:
√(2*2*7*a*a*b*c*c)
Using the property that the square root of a product is equal to the product of the square roots, we can rewrite the expression as:
√2 * √2 * √7 * √a * √a * √b * √c * √c
Simplifying further, we have:
2√(7a²bc²)
Therefore, the square root of 14abc times the square root of 2ab simplifies to 2√(7a²bc²).