Question 77913
{{{sqrt(63)-2*sqrt(28)+5*sqrt(7)}}}
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In each square root look for factors that are squares.
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{{{sqrt(9*7)- 2*sqrt(4*7)+5*sqrt(7)}}}
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Notice that 9 in the first square root and 4 in the second square root are squares.
Split the squares using the product rule for square roots to get:
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{{{sqrt(9)*sqrt(7) - 2*sqrt(4)*sqrt(7) + 5*sqrt(7)}}}
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Take the square root of 9 and the square root of 4 to reduce the expression to:
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{{{3*sqrt(7) - 2*2*sqrt(7) + 5*sqrt(7)}}}
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Multiply the 2*2:
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{{{3*sqrt(7) - 4*sqrt(7) + 5*sqrt(7)}}}
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Factor the {{{sqrt(7)}}} from each of the three terms to get:
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{{{(3 - 4 + 5)*sqrt(7)}}}
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Combine the terms inside the parentheses to get +4 and the expression finally becomes:
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{{{4*sqrt(7)}}}
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That's the answer. Cheers!