9.1- 9.6 Review

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: a² + b² = c².

Front

How do you find the height of a ladder leaning against a wall?

Back

To find the height of a ladder leaning against a wall, use the Pythagorean theorem. If the distance from the wall is 'a' and the length of the ladder is 'c', then the height 'b' can be found using b = √(c² - a²).

Front

What is the approximate value of √77?

Back

The square root of 77 is approximately between 8 and 9, since 8² = 64 and 9² = 81.

Front

How do you solve the equation 5b² - 4 = 41?

Back

To solve 5b² - 4 = 41, first add 4 to both sides to get 5b² = 45. Then divide by 5 to get b² = 9. Finally, take the square root to find b = 3 or b = -3.

Front

What is a non-perfect square?

Back

A non-perfect square is a number that cannot be expressed as the square of an integer. For example, 77 is a non-perfect square because there is no integer that, when squared, equals 77.

Front

What fraction is equivalent to 0.7?

Back

0.7 is equivalent to the fraction 7/10.

Front

What is the definition of a perfect square?

Back

A perfect square is an integer that is the square of another integer. For example, 1, 4, 9, and 16 are perfect squares.

Front

How do you determine if a number is a perfect square?

Back

To determine if a number is a perfect square, find its square root. If the square root is an integer, then the number is a perfect square.

Front

What is the relationship between fractions and decimals?

Back

Fractions and decimals are two ways to represent the same value. For example, 1/2 is equivalent to 0.5.

Front

How do you convert a decimal to a fraction?

Back

To convert a decimal to a fraction, write the decimal over 1, then multiply the numerator and denominator by 10 for each digit after the decimal point. Simplify if necessary.