Simplify the radical expression. EXPLAIN ALL YOUR STEPS. sqrroot 363-3sqrroot 27

Mathematics

1 answer:

Jobisdone [24]3 years ago

7 0

Answer:

2√3

Step-by-step explanation:

$\tt\sqrt{363}-3\sqrt{27}= \sqrt{11^2\cdot3}-3\sqrt{3^2\cdot3}= 11\sqrt{3}-9\sqrt{3}=2\sqrt{3}$

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Simplify the radical expression.

tresset_1 [31]

To simplify this fraction, multiply the entire fraction by the conjugate of the denominator. The conjugate of a square root and a number being added to it would be the number <em>subtracted </em>from the square root. In other words, the conjugate of $\sqrt{a} + b$ would be $\sqrt{a} - b$ .

Applying that information to our fraction shown here, the conjugate of the denominator would be $\sqrt{3} - 4$ . We will multiply both the numerator and denominator of our original fraction by this expression to obtain our answer, as shown below.