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3 years ago

What is the simplified form of the following expression? 5sqrt 8-sqrt18-2sqrt2

Mathematics

2 answers:

spayn [35]3 years ago

7 0

Answer:

5 sqrt2.

Step-by-step explanation:

sqrt8 = sqrt4 * sqrt2 = 2 sqrt2

sqrt18 = sqrt9 * sqrt2 = 3 sqrt2

So simplifying:

5sqrt 8 - sqrt18 - 2 sqrt2

= 5*2sqrt2 - 3 sqrt 2 - 2 sqrt2

= 10 sqrt2 - 5 sqrt2

= 5 sqrt2 (answer).

Y_Kistochka [10]3 years ago

5 0

For this case we must simplify the following expression:

$5 \sqrt {8} - \sqrt {18} -2 \sqrt {2}$

Rewriting we have:

$8 = 2 * 2 * 2 = 2 ^ 2 * 2\\18 = 9 * 2 = 3 ^ 2 * 2\\5 \sqrt {2 ^ 2 * 2} - \sqrt {3 ^ 2 * 2} -2 \sqrt {2} =$

We have that by definition of properties of roots and powers it is fulfilled:

$\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}$

So:

$5 * 2 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -5 \sqrt {2} =\\5 \sqrt {2}$

Answer:

$5 \sqrt {2}$

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