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Simplify with steps7√3 + 10√108

User IoctlLR
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1 Answer

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We need to use the following property of radicals to solve this question:


√(a\cdot b)=√(a)√(b)

The expression given is:


7√(3)+10√(108)

If we want to simplify, we need to rewrite the second term in terms of sqrt(3). We know that 108 is divisible by 3 because the sum of its digits is also divisible by 3.

Then:


(108)/(3)=36

We can rewrite:


7√(3)+10√(108)=7√(3)+10√(36\cdot3)

Using the property above:


7√(3)+10√(36)√(3)=7√(3)+10\cdot6√(3)

Now, we can simplify:


7√(3)+60√(3)=67√(3)

Thus, the answer is:


7√(3)+10√(108)=67√(3)

User Phnghue
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