WEBVTT
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Find the value of đť‘Ą for which root 1225 is equal to root 400 plus root đť‘Ą.
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Okay, to solve this problem, obviously we need to find the root of 1225 and square root of 400 to enable us to then figure out what đť‘Ą would be.
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Using a calculator, weâ€™ve just found the values of the square root of 1225 cause that would be 35, and weâ€™d also know that the square root of 400 would be 20.
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Iâ€™m also gonna show you quickly how youâ€™d do it if it was a non-calculator paper.
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If it was on a non-calculator paper, the part that might actually cause you a bit of trouble would be the square root of 1225 cause you may know itâ€™s 35, thatâ€™s great if you do.
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But if you donâ€™t, Iâ€™m just gonna show you how you can actually find it another way.
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To do it, weâ€™d actually use this rule which says that root đť‘Ž multiplied by root đť‘Ź is equal to root đť‘Žđť‘Ź.
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Now, to consider what the two values would be, we can actually look at 1250.
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Well, 1250 is equal to five multiplied by 250, but neither of those here would give us any square numbers.
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So letâ€™s remember the one weâ€™re trying to simplify, as said we wanted, is a square number.
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Okay, so then we can look at 50 multiplied by 25.
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We see actually yeah, 1250 would be made by 50 multiplied by 25.
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Great so long as you got a 25, thatâ€™s one of our square numbers.
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Now you think, right, well thatâ€™s 1250.
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If we wanted 1225, well thatâ€™s actually 25 less.
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So thatâ€™s gonna be equal to 25 multiplied by 49 cause I said one less than 50.
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Great.
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So now, here we actually have two square numbers.
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So we can now work out the value of the square root of 1225 cause root 25 is five, square root of 49 is seven.
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So then we multiply five and seven, and we get 35.
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I mean, looks that thatâ€™s just one way of looking at how you solve this problem without a calculator.
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And itâ€™s got a bit of trial and error, a bit of actually problem solving there.
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But now we may head back to the question.
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There, weâ€™ve got the values of the square roots of 1225 and 400 to solve.
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Okay.
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So first thing we do is subtract 20 from each side which gives us 15 is equal to root đť‘Ą.
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And next, we are to square each side.
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And then once weâ€™ve done that, weâ€™re gonna find the value of 15 squared.
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So there we have it; our final answer: đť‘Ą is equal to 225.