Multiply & simplify
Assume that all expressions under the radicals represent non negative numbers...
√5x^7 √35x
To multiply and simplify the expression √(5x^7) * √(35x), you can apply the rules of exponents and radicals.
Step 1: Multiply the numbers under the square root sign together: 5 * 35 = 175.
Step 2: Multiply the variables with the same base, x, together: x^7 * x = x^8.
Step 3: Place the product from steps 1 and 2 under the square root sign: √(175x^8).
Therefore, the simplified expression is √(175x^8).
To multiply and simplify the given expression √(5x^7) * √(35x), we can use the property of radicals that states √(a) * √(b) = √(a * b).
Step 1: Multiply the coefficients
The coefficient of the first radical is √5.
The coefficient of the second radical is √35.
√5 * √35 = √(5 * 35) = √175
Step 2: Multiply the variables
The variable under the first radical is x^7.
The variable under the second radical is x.
x^7 * x = x^(7+1) = x^8
Therefore, the simplified expression is:
√5x^7 * √35x = √175x^8