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.