91Ó°ÊÓ

Find each product. Which one of the following radicals is simplified? A. \(\sqrt{47}\) B. \(\sqrt{45}\) c. \(\sqrt{48}\) D. \(\sqrt{44}\)

Simplify each radical. $$ \sqrt{125} $$

Simplify each radical. $$ \sqrt{145} $$

Concept Check The first step in solving the equation $$ \sqrt{2 x+1}=x-7 $$ is to square each side of the equation. Errors often occur in solving equations such as this one when the right side of the equation is squared incorrectly. What is the square of the right side?

To rationalize the denominator of an expression such as \(\frac{4}{\sqrt{3}},\) we multiply both the numerator and denominator by \(\sqrt{3}\). By what number are we actually multiplying the given expression, and what property of real numbers justifies the fact that our result is equal to the given expression?

Find each product and simplify. $$ \sqrt{9} \cdot \sqrt{50} $$

Solve each equation. $$ \sqrt{3 x}+6=x $$

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 5. $$ -\sqrt{64} $$

Determine whether each number is rational, irrational, or not a real number. If a number is rational, give its exact value. If a number is irrational, give a decimal approximation to the nearest thousandth. Use a calculator as necessary. See Examples 4 and 5. $$ -\sqrt{500} $$

Find each product and simplify. $$ 5 \sqrt{6} \cdot 2 \sqrt{10} $$