Can you teach me how to use a mathematical table to find the square root, squares and cubes of numbers

Find the number whose square you want to find in the main column (usually labeled "N" or "Number").

Once you've found your number, look across the row to the column labeled "Squares" (or $N^2$). The value there is the square of your number.

Example: Find the square of 25.

1. Locate 25 in the "Number" column.
2. Read the value in the "Squares" column corresponding to 25. It will be 625. So, $25^2 = \boxed{625}$.

How to find Square Roots using a Mathematical Table

Mathematical tables have sections for "Square Roots" which are often divided into $\sqrt{N}$ and $\sqrt{10N}$ to handle numbers of different magnitudes.

• If the number has an odd number of digits before the decimal point (e.g., 4, 144, 2.5), use the $\sqrt{N}$ column.
• If the number has an even number of digits before the decimal point (e.g., 16, 2500, 0.36), use the $\sqrt{10N}$ column.
• For numbers between 1 and 100, if the number is between 1 and 9.99, use $\sqrt{N}$. If it's between 10 and 99.9, use $\sqrt{10N}$.

Find the number (or its significant digits) in the "Number" column.

Read the value in the $\sqrt{N}$ or $\sqrt{10N}$ column corresponding to your number. Adjust the decimal point based on the original number's magnitude.

Example 1: Find the square root of 64.

1. 64 has an even number of digits (two) before the decimal point. Use the $\sqrt{10N}$ column.
2. Locate 64 in the "Number" column.
3. Read the value in the $\sqrt{10N}$ column. It will be 8.000. So, $\sqrt{64} = \boxed{8}$.

Example 2: Find the square root of 2.25.

1. 2.25 has an odd number of digits (one) before the decimal point. Use the $\sqrt{N}$ column.
2. Locate 2.25 (or 225 and adjust) in the "Number" column.
3. Read the value in the $\sqrt{N}$ column. It will be 1.500. So, $\sqrt{2.25} = \boxed{1.5}$.

How to find Cubes using a Mathematical Table

Mathematical tables usually have a section for "Cubes."

Find the number whose cube you want to find in the main column (usually labeled "N" or "Number").

Once you've found your number, look across the row to the column labeled "Cubes" (or $N^3$). The value there is the cube of your number.

Example: Find the cube of 4.

1. Locate 4 in the "Number" column.
2. Read the value in the "Cubes" column corresponding to 4. It will be 64. So, $4^3 = \boxed{64}$.