WEBVTT
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Without using a calculator, order the numbers 𝜋, root two, one, two, and root three from smallest to largest.
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Now, in order to put our numbers in order without a calculator, what we need to do is find the numerical values of three of our numbers.
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And that’s 𝜋, root two, and root three.
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Well, first of all, we have 𝜋.
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Well, we know that 𝜋 is equal to 3.14 et cetera.
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So that’s the value of 𝜋.
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So we know that one.
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Well, next, we need to consider root two.
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Well, to enable us to consider root two, what we can consider is the two square numbers either side of root two.
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So we’ve got one and four.
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Now, if we take the root of one and the root of four, we get the answers one and two.
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So therefore, we can say that root two is gonna be between one and two.
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So we can say that root two is greater than one, but less than two.
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And then again, we can use the same principle for root three because root three must be less than two.
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And that’s because root four is equal to two, but it also must be greater than root two because the square root of three is gonna be a larger number than the square root of two.
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So now, what we can do is use these properties or these estimates for our values to help us to order the numbers.
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So we want to order them.
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When looking at the question from smallest to largest, so therefore our smallest number is going to be one because we know that root two is greater than one.
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Then, our next value is going to be root two.
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And that’s because we know that root two is greater than one, but less than root three.
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Then, our next value will be root three cause we’ve shown that root three is greater than root two, but less than two.
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Then, we have two because again we’ve shown that two is greater than root three.
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But two is less than 𝜋 because it’s less than 3.14.
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So therefore, our final value is 𝜋.
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So we can say that without using a calculator, we’ve ordered the numbers 𝜋, root two, one, two, and root three from smallest to largest.
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And they are one, root two, root three, two, and 𝜋.