Question

Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality. ____< (Square root of) 32 <______

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Answer 1

5<square root of 32<6

Step-by-step explanation

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Answer 2

`\boxed{5} < √(32) < \boxed{6}`

Explanation:

To find the two consecutive integers that √(32) is between, we need to find the perfect squares that are above and below the square of √(32).

An integer is a whole number that can be either positive, negative, or zero, without any fractional or decimal parts.

A perfect square is a number that can be obtained by multiplying an integer by itself.

The first few perfect squares are:

• 1² = 1
• 2² = 4
• 3² = 9
• 4² = 16
• 5² = 25
• 6² = 36

The square of √(32) is 32.

The number 32 is between the perfect squares 25 and 36:

• 25 < 32 < 36

Taking the square roots of each number in the inequality gives:

• 5 < √(32) < 6

Therefore, the two consecutive integers that complete the given inequality are 5 and 6.