Math  /  Numbers & Operations

Question1. 5\sqrt{5} is between 3.

Studdy Solution

STEP 1

1. We need to find two consecutive integers between which 5\sqrt{5} lies.
2. We will use the property that n\sqrt{n} is between two integers aa and bb if a2<n<b2a^2 < n < b^2.

STEP 2

1. Identify the integers.
2. Verify the placement of 5\sqrt{5}.

STEP 3

Identify two consecutive integers aa and bb such that a2<5<b2a^2 < 5 < b^2.

STEP 4

Calculate the squares of integers around 5 to find the appropriate range.
22=4 2^2 = 4 32=9 3^2 = 9
Since 4<5<94 < 5 < 9, 5\sqrt{5} is between 2 and 3.

STEP 5

Verify that 5\sqrt{5} is indeed between 2 and 3 by checking the inequalities.
2<5<3 2 < \sqrt{5} < 3
The solution to the problem is that 5\sqrt{5} is between:
2 and 3\boxed{2 \text{ and } 3}

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