Question Video: Solving Quadratic Equations Using Estimation Mathematics • 8th Grade

Estimate the solution of the following equation to the nearest integer: 𝑑² = 68.


Video Transcript

Estimate the solution of the following equation to the nearest integer: 𝑑 squared equals 68.

So we have the equation 𝑑 squared equals 68. Now it said to estimate the solution. So maybe this is because, say, maybe we didn’t have a calculator. So 𝑑 squared equals 68. To solve for 𝑑, we would have to square root both sides.

So the issue is we don’t necessarily know the square root of 68 because it’s not a perfect square. So we need to figure out what 𝑑 would be equal to. So what are some perfect squares that are close to 68 that we know?

Let’s look on a number line. So if we put 68 relatively in the middle, so to the left of 68 is 64. The square root of 64 is equal to eight. So what would be a perfect square to the right of 68 on the number line? That would be 81. The square root of 81 is nine.

So is 68 closer to 64 or 81? 68 is much closer to 64. So if we were to estimate to the nearest integer. And integers are zero, one, two, three, four, the zeros to the positives and the negatives.

So we would estimate eight. Now since it’s an integer, integers also include the negatives. So it’s true that eight squared is 64. But it’s also true that negative eight squared is equal to 64.

So our estimate would be 𝑑 equals eight or 𝑑 equals negative eight, since 68 was so close to 64 and the square root of 64 was eight.

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