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Express root 15 multiplied by 11 root five plus two root three in its simplest form.
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In order to simplify this expression, we need to use some of the laws of surds.
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Root π multiplied by root π is equal to π.
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Root π multiplied by root π is equal to root of ππ.
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And root π multiplied by π is equal to π root π.
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In order to expand or multiply out the parenthesis, we need to multiply root 15 by 11 root five and then root 15 by two root three.
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Letβs first consider root 15 multiplied by 11 root five.
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Root 15 can be split into root three multiplied by root five, as three multiplied by five is 15.
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11 root five can be rewritten as 11 multiplied by root five.
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Using the law of surds root π multiplied by root π is equal to π, we can see that root five multiplied by root five is equal to five.
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This gives us root three multiplied by five multiplied by 11.
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As five multiplied by 11 is 55, the first expression becomes 55 root three.
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Root 15 multiplied by 11 root five is 55 root three.
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Now letβs consider the second part of the expansion, root 15 multiplied by two root three.
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If we split the two terms in the same way as the first part, weβre left with root three multiplied by root five multiplied by two multiplied by root three.
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Root three multiplied by root three is equal to three.
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So we now have three multiplied by root five multiplied by two.
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This is equal to six root five.
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Therefore, root 15 multiplied by two root three is equal to six root five.
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Root 15 multiplied by 11 root five plus two root three in its simplest form is written 55 root three plus six root five.