Home w (3+sqrt7)(4-sqrt13)

Apply Distributive Property: First, we'll use the distributive property (FOIL method) to multiply these two binomials. (3+sqrt7)(4-sqrt13) = 3*4 + 3*(-sqrt13) + sqrt7*4 - sqrt7*sqrt13Multiply Numbers: Now, let's multiply the numbers. 3*4 = 12 3*(-sqrt13) = -3sqrt13 sqrt7*4 = 4sqrt7 -sqrt7*sqrt13 = -sqrt(7*13)Combine Calculated Terms: Next, we combine all the terms we've calculated. 12 - 3sqrt13 + 4sqrt7 - sqrt(7*13)Simplify Last Term: We simplify the last term, sqrt(7*13). -sqrt(7*13) = -sqrt(91)Write Simplified Expression: Finally, we write down the simplified expression. 12 - 3sqrt13 + 4sqrt7 - sqrt(91)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Home w $\newline$ $(3+\sqrt{7})(4-\sqrt{13})$

View step-by-step help

Home

Math Problems

Algebra 1

Multiply radical expressions

Full solution

Q. Home w

\newline

(3+\sqrt{7})(4-\sqrt{13})

Apply Distributive Property: First, we'll use the distributive property (FOIL method) to multiply these two binomials. $\newline$ $(3+\sqrt{7})(4-\sqrt{13}) = 3\cdot 4 + 3\cdot (-\sqrt{13}) + \sqrt{7}\cdot 4 - \sqrt{7}\cdot\sqrt{13}$
Multiply Numbers: Now, let's multiply the numbers. $\newline$ $3 \times 4 = 12$ $\newline$ $3 \times (-\sqrt{13}) = -3\sqrt{13}$ $\newline$ $\sqrt{7} \times 4 = 4\sqrt{7}$ $\newline$ $-\sqrt{7} \times \sqrt{13} = -\sqrt{7 \times 13}$
Combine Calculated Terms: Next, we combine all the terms we've calculated. $12 - 3\sqrt{13} + 4\sqrt{7} - \sqrt{7\times13}$
Simplify Last Term: We simplify the last term, $\sqrt{7\times13}$ . $-\sqrt{7\times13} = -\sqrt{91}$
Write Simplified Expression: Finally, we write down the simplified expression. $12 - 3\sqrt{13} + 4\sqrt{7} - \sqrt{91}$