Problem 70
Question
Simplify the radical expression. $$ \sqrt{40} $$
Step-by-Step Solution
Verified Answer
\(\sqrt{40} = 2\sqrt{10}\)
1Step 1: Prime Factorization
Divide 40 into its prime factors. This would be \(2^3 * 5\). So, \( \sqrt{40} = \sqrt{2^3 * 5} \)
2Step 2: Simplify
From the prime factorization, recognize that \(2^2\) is a perfect square. So, extract it out of the root. This simplifies the expression to \(2 * \sqrt{2*5}\)
3Step 3: Final Simplification
Simplify the remaining product in the root, which is \(2*5\), to get 10. So, the final simplification of the square root is \(2 * \sqrt{10}\)
Other exercises in this chapter
Problem 69
Evaluate the radical expression when a = 2 and b = 4. $$ \sqrt{b^{2}+10 a} $$
View solution Problem 69
Which quadratic equation is written in standard form? A. \(8 x+5 x^{2}-9=0\) B. \(5 x^{2}+8 x=9\) C. \(5 x^{2}+8 x-9=0\) D. \(9-8 x-5 x^{2}=0\)
View solution Problem 70
Write the radical expression in simplest form. $$ \sqrt{\frac{48}{81}} $$
View solution Problem 70
Evaluate the radical expression when a = 2 and b = 4. $$ \sqrt{b^{2}-8 a} $$
View solution