square root of 3x times square root of 7x^3
To simplify the expression √(3x) * √(7x^3), you can use the property of square roots that states √(a) * √(b) = √(a * b).
In this case, you have √(3x) * √(7x^3) which can be rewritten as √((3x) * (7x^3)).
To simplify the multiplication within the square root, you can apply the rules of exponents. Remember that when multiplying variables with the same base, you add their exponents.
So, (3x) * (7x^3) = 3 * 7 * x * x^3 = 21x * x^3 = 21x^4.
Now, substitute the simplified expression back into the square root: √(21x^4).
To further simplify, you can break down the exponent. The square root of x^4 is x^(4/2) which equals x^2.
So, √(21x^4) = √(21) * √(x^4) = √(21) * x^2.
Therefore, the simplified expression is √(3x) * √(7x^3) = √(21) * x^2.