Example 1

Express as an entire radical.

Step 1: Rewrite «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#0F1934¨»4«/mn»«msqrt mathcolor=¨#0F1934¨»«mn»7«/mn»«/msqrt»«/math» as an entire radical by squaring the 4 (taking it to the power of 2) and taking the square root of that value.

Step 2: Bring the 42 and the 7 under the same root sign and express the result as a product.

Step 3: Multiply the factors.



Example 2

Express «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mroot»«mn»9«/mn»«mn»3«/mn»«/mroot»«/math» as an entire radical.

Step 1: Rewrite «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#0F1934¨»2«/mn»«mroot mathcolor=¨#0F1934¨»«mn»9«/mn»«mn»3«/mn»«/mroot»«/math» as an entire radical by cubing the 2 (taking it to the power of 3) and taking the cube root of that value.

Step 2: Bring the 23 and the 9 under the same root sign and express the result as a product.

Step 3: Multiply the factors.