Video: Simplifying Numerical Expressions Using Properties of Square Roots

Simplify (√2 + 9)(−5 + √2).

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Video Transcript

Simplify root two plus nine multiplied by negative five plus root two.

In order to simplify this expression, we’ll use the FOIL method to expand or multiply out our parentheses. Our first step is to multiply root two by negative five. This gives us negative five root two. Next, we’ll multiply the outside terms: root two multiplied by root two. This gives us root four, which is equal to two.

We will then multiply the inside terms: positive nine multiplied by negative five. This is equal to negative 45. And finally, we’ll multiply the last terms. Nine multiplied by root two is nine root two. We can then group or simplify the like terms.

Grouping the rational terms, positive two minus 45 gives us negative 43. And grouping the irrational terms or surds gives us positive four root two, as negative five root two plus nine root two is equal to four root two. This means that root two plus nine multiplied by negative five plus root two is equal to negative 43 plus four root two.

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