Estimating Roots

Front

What is the square root of a number?

Back

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 x 3 = 9.

Front

How do you estimate the square root of a number?

Back

To estimate the square root of a number, find two perfect squares between which the number lies. For example, to estimate √50, note that 49 (7²) and 64 (8²) are perfect squares, so √50 is between 7 and 8.

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction. Its decimal representation goes on forever without repeating. Examples include √2 and π.

Front

How can you compare irrational numbers?

Back

To compare irrational numbers, estimate their values by finding their approximate square roots or using a calculator. For example, √8 is approximately 2.83 and √10 is approximately 3.16.

Front

What is the area of a square?

Back

The area of a square is calculated by squaring the length of one of its sides. If the side length is 's', then the area A = s².

Front

How do you find the side length of a square given its area?

Back

To find the side length of a square given its area, take the square root of the area. For example, if the area is 36 square meters, the side length is √36 = 6 meters.

Front

What is the approximate value of √27?

Back

The approximate value of √27 is about 5.2, since 5² = 25 and 6² = 36.

Front

Which is greater: √63 or 7.5?

Back

√63 is approximately 7.94, which is greater than 7.5.

Front

How do you list numbers from least to greatest?

Back

To list numbers from least to greatest, compare their values and arrange them in ascending order. For example, -64, 3.5, √27, 6.666... would be the correct order.

Front

What is the closest irrational number to 4?

Back

The closest irrational number to 4 among the options given is √17, which is approximately 4.12.