To determine between which two consecutive whole numbers $\sqrt{53}$ lies, we can first find the square roots of numbers close to 53 that are perfect squares.

Step 1: Identifying the perfect squares closest to 53

• $\sqrt{49} = 7$ (since $7^2 = 49$)
• $\sqrt{64} = 8$ (since $8^2 = 64$)

Thus, we know that: $7^2 = 49 \quad \text{and} \quad 8^2 = 64$ So, $\sqrt{53}$ lies between 7 and 8.

Step 2: Approximation

Since 53 is closer to 49 than 64, $\sqrt{53}$ is closer to 7 than 8 but still between these two whole numbers.

Final Answer:

The square root of 53 lies between 7 and 8. Therefore, the correct sentence would be:

"Since $\sqrt{49} = 7$ and $\sqrt{64} = 8$, it is known that $\sqrt{53}$ is between 7 and 8."

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Would you like to go into more detail about approximating square roots?

Here are 5 questions to further explore this topic:

1. What is the approximate value of $\sqrt{53}$ to one decimal place?
2. How would you estimate the square root of non-perfect square numbers?
3. What methods can be used to find more precise square root values?
4. How can the concept of perfect squares help in estimating square roots?
5. What are some real-world applications of estimating square roots?

Tip: When estimating square roots of non-perfect squares, always find the perfect squares on either side of the number!