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Combine these radicals. 8 square root 5 + 2 square root 45

Sagot :

civilmatthania5

Answer

14√5

Step-by-step explanation:

8√5 + 2√45

= 8√5 + 6√5

= 14√5

Hope this helps

Sarah06109

Answer:

[tex]\boxed {\boxed {\sf 14 \sqrt{5}}}[/tex]

Step-by-step explanation:

We are asked to combine the radicals. We have the following expression:

[tex]8 \sqrt{5} + 2 \sqrt{45}[/tex]

Currently, we cannot combine these radicals. The value under the square root is not the same for both terms.

However, we can simplify the radical 2 √45 because the value under the radical is divisible by a perfect square.

45 can be divided by 9 (the perfect square) for a quotient of 5. So, we can simplify the radical using this information.

Break the radical into 2 radicals: 9 and 5.

[tex]8 \sqrt{5}+ 2 \sqrt{9}\sqrt{5}[/tex]

Notice that a perfect square is under the radical. √9 can be simplifed to 3.

[tex]8 \sqrt{5}+ 2 *3 \sqrt{5}[/tex]

Multiply 2 and 3.

[tex]8 \sqrt{3} + 6 \sqrt{5}[/tex]

Now the value under the radical is the same for both terms, and we can add the numbers in front of the radicals.

[tex]14 \sqrt{5}[/tex]

The radicals combined is equal to 14√5

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