Math Problem Statement

can you solve all of these answers for me

Can you solve all of these answers for me?

Solution

Let's go through and solve each part of the worksheet.

1. Find the Square Roots:

  • Square root of 16:
    16=4\sqrt{16} = 4
  • Square root of 64:
    64=8\sqrt{64} = 8
  • Square root of 121:
    121=11\sqrt{121} = 11
  • Square root of 5 (estimated):
    5\sqrt{5} is between 2 and 3 because 22=42^2 = 4 and 32=93^2 = 9.
    A closer estimate would be approximately 2.23.

2. Filling in the Blanks:

  • Use your perfect square knowledge to find the whole numbers you are working between.

    You need to recognize perfect squares around the number to estimate its square root.

3. Steps to Estimate Roots:

  • Find perfect squares on either side of the number (a little more and a little less).

    For example, for 5\sqrt{5}, 4 and 9 are the perfect squares around 5.

  • Need a closer estimate? Look to see which perfect square is closer and estimate.

    For 5\sqrt{5}, since 5 is closer to 4 than to 9, the square root will be slightly greater than 2.

4. Example in Image:

  • 122=14412^2 = 144, which is shown in the example for calculating the square of a number.

5. Estimate to the Nearest Integer:

  • 23\sqrt{23} is between 4 and 5 because 42=164^2 = 16 and 52=255^2 = 25. It's closer to 5, so the estimate is about 5.
  • 18\sqrt{18} is between 4 and 5, as 42=164^2 = 16 and 52=255^2 = 25. It's closer to 4, so the estimate is about 4.
  • 150\sqrt{150} is between 12 and 13, as 122=14412^2 = 144 and 132=16913^2 = 169. It's closer to 12, so the estimate is about 12.

Would you like a detailed explanation on any of these answers or how square roots are estimated?

Here are 5 related questions you can try:

  1. What is the square root of 50 estimated between two integers?
  2. Can you find the square root of 10 using perfect squares?
  3. What is 225\sqrt{225}?
  4. Estimate the square root of 30 to the nearest integer.
  5. What is 81\sqrt{81} and 49\sqrt{49}?

Tip: When estimating square roots, always find the two closest perfect squares for more accurate guesses!

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Math Problem Analysis

Mathematical Concepts

Square Roots
Estimation
Perfect Squares

Formulas

√(number) = square root of a number
n² = number when squaring

Theorems

Perfect squares theorem: a number is a perfect square if it can be written as n²

Suitable Grade Level

Grades 6-8