Video: Simplifying Numerical Expressions Involving Square Roots

Simplify √6(−3 − √6) − 3(−6 + √6).

02:02

Video Transcript

Simplify root six multiplied by negative three minus root six minus three multiplied by negative six plus root six.

In order to simplify this expression, we need to use some of the laws of surds. Firstly, root 𝑎 multiplied by root 𝑎 is equal to 𝑎. Secondly, root 𝑎 multiplied by 𝑏, an integer, is equal to 𝑏 root 𝑎. And root 𝑎 multiplied by root 𝑏 is equal to root 𝑎 times 𝑏.

In order to simplify the expression, we need to expand or multiply out the parentheses. Root six multiplied by negative three is negative three root six. Root six multiplied by negative root six is equal to negative six. Moving on to the second bracket or parenthesis, negative three multiplied by negative six is positive 18. And finally, negative three multiplied by positive root six is negative three root six.

We then need to simplify this expression by grouping the like terms. Negative three root six minus three root six is equal to negative six root six. In the same way, negative six plus 18 is equal to positive 12. This means that our answer is negative six root six plus 12.

Simplifying root six multiplied by negative three minus root six minus three multiplied by negative six plus root six is equal to negative six root six plus 12.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.