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Inessa [10]
2 years ago
12

Combine the radicals 5sqrt27-17sqrt3

Mathematics
2 answers:
Bess [88]2 years ago
6 0

Answer:

-2 sqrt3.

Step-by-step explanation:

sqrt27 = sqrt9 * sqrt3

= 3 sqrt3   So:

5sqrt27 - 17sqrt3

= 5*3 sqrt3 - 17 sqrt 3

= 15 sqrt 3 - 17 sqrt 3

= -2 sqrt3.

kow [346]2 years ago
4 0

For this case we must simplify the following expression:

5 \sqrt {27} -17 \sqrt {3}

We have to:

27 = 3 * 3 * 3 = 3 ^ 2 * 3

Substituting in the expression we have:

5 \sqrt {3 ^ 2 * 3} -17 \sqrt {3}

For properties of powers and roots we have:

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

So:

5 * 3 \sqrt {3} -17 \sqrt {3} =\\15 \sqrt {3} -17 \sqrt {3} =

We subtract taking into account that different signs are subtracted and the sign of the major is placed:

-2 \sqrt {3}

Answer:

-2 \sqrt {3}

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