x is a positive number. If it’s rational, plot its exact value on a number line. If it’s irrational, find an approximate location for x on a number line.Start by thinking of the value of x. What is one way to represent the value of x? Use square root notation to write your answer.x 2 = 72x = √72Great job!Now, think about the value of 72 . Is it equal to a whole number? In other words, is there any whole number you can square, or multiply by itself, to get a product of 72?x 2 = 72 x = 72 Yes, 72 is equal to a whole number.No, 72 is not equal to a whole number.Great job!72 is not equal to a whole number because there is no whole number that we can multiply by itself to find a product of 72. 72 is irrational, so we can only find an approximation of its value. Which point below could represent the location on the number line for that approximate value?x 2 = 72x = 72 012345678910ABCDPoint APoint BPoint CPoint DGood work!Now that you’ve plotted x on the number line, consider another variable below, y. Which point could represent the approximate location of y on the number line? y = − 72 -10-9-8-7-6-5-4-3-2-1012345678910
Question
x is a positive number. If it’s rational, plot its exact value on a number line. If it’s irrational, find an approximate location for x on a number line.Start by thinking of the value of x. What is one way to represent the value of x? Use square root notation to write your answer.x 2 = 72x = √72Great job!Now, think about the value of 72 . Is it equal to a whole number? In other words, is there any whole number you can square, or multiply by itself, to get a product of 72?x 2 = 72 x = 72 Yes, 72 is equal to a whole number.No, 72 is not equal to a whole number.Great job!72 is not equal to a whole number because there is no whole number that we can multiply by itself to find a product of 72. 72 is irrational, so we can only find an approximation of its value. Which point below could represent the location on the number line for that approximate value?x 2 = 72x = 72 012345678910ABCDPoint APoint BPoint CPoint DGood work!Now that you’ve plotted x on the number line, consider another variable below, y. Which point could represent the approximate location of y on the number line? y = − 72 -10-9-8-7-6-5-4-3-2-1012345678910
Solution
The question seems to be incomplete and a bit confusing. However, I'll try to answer based on the information given.
First, we have x^2 = 72, which means x = sqrt(72). The square root of 72 is approximately 8.48, which is an irrational number. So, on a number line from 0 to 10, x would be located between 8 and 9, closer to 8.
Next, we have y = -sqrt(72). The negative square root of 72 is approximately -8.48. So, on a number line from -10 to 10, y would be located between -9 and -8, closer to -9.
Please note that these are approximate locations because sqrt(72) and -sqrt(72) are irrational numbers.
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