Simplify square root of 16x+ square root of x^5

Problem

√(,16*x)+√(,x5)

Solution

1. Apply the product property of radicals to the first term by splitting the square root of the product into the product of the square roots.

√(,16*x)=√(,16)⋅√(,x)

2. Evaluate the square root of the constant coefficient in the first term.

√(,16)⋅√(,x)=4√(,x)

3. Rewrite the radicand of the second term using the highest even power of x to prepare for simplification.

√(,x5)=√(,x4⋅x)

4. Simplify the radical of the second term by taking the square root of the even power.

√(,x4⋅x)=x2√(,x)

5. Combine the simplified terms into a single expression.

4√(,x)+x2√(,x)

6. Factor out the common radical √(,x) to reach the final simplified form.

(4+x2)√(,x)

Final Answer

√(,16*x)+√(,x5)=(4+x2)√(,x)

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