WEBVTT
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Replace π₯ by a positive number to make 16 ninths equals π₯ squared true.
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So in order to solve for π₯, we need to isolate π₯.
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We need to get rid of this squared, the exponent of two.
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So the inverse of squaring a number would be to square-root a number.
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So we need to square-root both sides.
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So we have to square root of 16 ninths equals π₯.
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Now when taking the square root of a fraction, we can separate the numerator and the denominator as separate square roots.
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So instead, we could have the square root of 16 divided by the square root of nine equals π₯.
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Now the square root of 16 we can put it on our calculator.
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And we get four.
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And technically, the square root of 16 is positive four and negative four.
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And then the square root of nine is positive three and negative three.
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However, it says to replace π₯ with a positive number.
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So we only want the positives.
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Therefore, π₯ will be replaced with four-thirds.
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So to double check, we can always plug our answer back in.
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So the original question said 16 ninths equals π₯ squared.
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So letβs replace π₯ with four-thirds.
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So now we need to square four-thirds.
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So we need to square the four and square the three.
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And four squared is 16.
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And three squared is nine.
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So therefore, four-thirds is our correct answer.