2.7 Square Roots & Comparing Real Numbers

Square Root a number times itself to make the number you started with

Radicand the number under the radical symbol

Perfect Square the square of an integer

Irrational Number a number that is not rational

Real Number the set of all rational and irrational numbers

Find square roots

EXAMPLE 1:The positive square root of 49 is 7.The negative square root of 4 is 2.Evaluate the expression.

GUIDED PRACTICEThe negative square root of 9 is -3 The positive square root of 25 is 5.The positive and negative square root of 64 as 8 and 8.Evaluate the expression.The negative square root of 81 is -9

Approximate a square rootEXAMPLE 2:FURNITURESOLUTION

Approximate a square root

EXAMPLE 2:As shown in the table, 945 is not a perfect square. The greatest perfect square less than 945 is 900. The least perfect square greater than 945 is 961.900 < 945 < 961

Number2829303132Square of number7848419009611024

Approximate a square root

EXAMPLE 2:

As shown in the table, 32 is not a perfect square. The greatest perfect square less than 32 is 25. The least perfect square greater than 25 is 36.Approximate the square root to the nearest integer.You can use a table to determine whether 32 is a perfect square. GUIDED PRACTICE

25 < 32 < 36Write a compound inequality that compares 32 with both 25 and 36.Take positive square root of each number.Find square root of each perfect square.GUIDED PRACTICE

As shown in the table, 103 is not a perfect square. The greatest perfect square less than 103 is 100. The least perfect square greater than 100 is 121.Approximate the square root to the nearest integer.You can use a table to determine whether 103 is a perfect square. GUIDED PRACTICE

Number89101112Square of number6481100121144

100< 103< 121Write a compound inequality that compares 103 with both 100 and 121.Take positive square root of each number.Find square root of each perfect square.GUIDED PRACTICE

As shown in the table, 48 is not a perfect square. The greatest perfect square less than 48 is 36. The least perfect square greater than 48 is 49.Approximate the square root to the nearest integer.You can use a table to determine whether 48 is a perfect square. GUIDED PRACTICE

36 < 48 < 49Write a compound inequality that compares 103 with both 100 and 121.Take positive square root of each number.Find square root of each perfect square.GUIDED PRACTICE

As shown in the table, 350 is not a perfect square. The greatest perfect square less than 350 is 324. The least perfect square greater than 350 is 361.Approximate the square root to the nearest integer.You can use a table to determine whether 48 is a perfect square. GUIDED PRACTICE

324 < 350 < 361Write a compound inequality that compares 350 with both 324 and 361.Take positive square root of each number.Find square root of each perfect square.

Classify numbers

EXAMPLE 3:

Graph and order real numbers

EXAMPLE 4:SOLUTIONBegin by graphing the numbers on a number line.

SOLUTIONBegin by graphing the numbers on a number line.GUIDED PRACTICERead the numbers from left to right:Order the numbers from least to greatest:

GUIDED PRACTICEClassify the following numbers as Real, Rational, Irrational, Integer and/or Whole:

Real?Rational?Irrational?Integer?Whole?-2.54/3