Between which two consecutive integers is -√26? Do not use a calc...

Question

Between which two consecutive integers is -√26? Do not use a calculator.

Accepted Answer

Hey, everyone in this problem, we're asked to determine the pair of consecutive integers where negative square root of 53 is found in between. We're given four answer choices. Option A negative six and negative five. Option B negative seven and negative six. Option C negative eight and negative seven and option D negative nine and negative eight. Now we're given some possible integers in our answer choices. So we have negative five down to negative nine. So let's think about how we could write these as square roots so that we can compare this to the value we were given in the problem starting with the lowest if we wanna write negative five. Well, we know that five is equal to the square root of 25. So this can be rewritten as negative the square root of 25. We can do the same for negative six. We know that six is equal to the square root of 36. So negative six can be rewritten as negative the square root of 36. We're gonna keep doing this for those other values until we can figure out where negative square root of 53 falls negative seven. And we know that seven squared is equal to 49. So the square root of 49 is equal to seven. So we can write negative seven as negative the square root of 49. Again, for negative eight, eight squared is 64. That means we can rank the square root of 64 as eight. And so negative eight is equal to negative the square root of 64. I'm gonna stop there. Now we have negative the square root of 49 and negative the squared of 64. Now 53 lies between 49 and 64. And so the square, negative square root of 53 is also going to be between negative the square root of 49 and negative the square root of 64. Which means that the result is going to be somewhere between negative seven and negative eight. OK. If we compare this with our answer choices, we found that negative, the square of 53 is between negative eight and negative seven that corresponds with answer choice. C Thanks everyone for watching. I hope this video helped see you in the next one.

Between which two consecutive integers is -√26? Do not use a calculator.

Key Concepts

Square Roots

Estimating Square Roots

Consecutive Integers

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