Question #66f34

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Answer 1 · 2017-09-01T01:09:55

Split up radical into equal terms and simplify any perfect squares. Multiply it with the coefficient.

To simplify a radical, we can "split up" the radical into perfect squares.

Let's just ignore the $7$ $7$ completely for now and just focus on the radical.

Do you agree that $\sqrt{50} = \sqrt{25} \sqrt{2}$ $sqrt50 = sqrt25sqrt2$ ? Check your calculator.

Notice how $\sqrt{25} = 5$ $sqrt25=5$ . Therefore, we can simplify the expression like so:

$7 \sqrt{50}$ $7sqrt50$

$= 7 \sqrt{25} \sqrt{2}$ $=7sqrt25sqrt2$

$= 7 (5) \sqrt{2}$ $=7(5)sqrt2$

$= 35 \sqrt{2}$ $=35sqrt2$

Keep in mind that these terms are all being multiplied with one another.

We can check our work by using a calculator and comparing answers.

$7 \sqrt{50} = 49.49747468$ $7sqrt50=49.49747468$

$35 \sqrt{2} = 49.49747468$ $35sqrt2=49.49747468$

The expression has now been simplified, since it cannot be simplified any more.

Hope this helps :)