Which of the numbers given below is the square root of 15376?
124
Understanding the Square Root Problem
The question asks us to find the number which, when multiplied by itself, gives 15376. This number is called the square root of 15376.
Finding the square root of a number means determining the base number that was squared (multiplied by itself) to get the original number. For example, the square root of 25 is 5 because \(5 \times 5 = 25\).
Finding the Square Root of 15376
We are given four options, and the easiest way to solve this problem is to check each option by squaring it (multiplying the number by itself) and seeing which one results in 15376.
Method: Checking the Options
Let's take each option and calculate its square:
| Option | Calculation (Square) | Result | Comparison with 15376 |
|---|---|---|---|
| 128 | \(128 \times 128\) | 16384 | \(16384 \neq 15376\) |
| 134 | \(134 \times 134\) | 17956 | \(17956 \neq 15376\) |
| 122 | \(122 \times 122\) | 14884 | \(14884 \neq 15376\) |
| 124 | \(124 \times 124\) | 15376 | \(15376 = 15376\) |
Analysis of Results
From the table above, we can see the result of squaring each option:
- Squaring 128 gives 16384.
- Squaring 134 gives 17956.
- Squaring 122 gives 14884.
- Squaring 124 gives 15376.
The number 124, when squared, results in 15376. This means that 124 is the square root of 15376.
Therefore, \(\sqrt{15376} = 124\).
Revision Table: Key Square Root Facts
| Term | Definition | Example |
|---|---|---|
| Square | The result of multiplying a number by itself (n\(\times\)n or n2). | The square of 7 is \(7 \times 7 = 49\). |
| Square Root | A number that, when squared, gives the original number. Denoted by \(\sqrt{}\). | The square root of 49 is 7, written as \(\sqrt{49} = 7\). |
| Perfect Square | An integer that is the square of an integer (e.g., 1, 4, 9, 16, 25...). | 15376 is a perfect square because its square root (124) is an integer. |
Additional Information: Estimating Square Roots
Before checking options, you can sometimes estimate the square root. For 15376:
- We know \(100 \times 100 = 10000\).
- We know \(130 \times 130 = 16900\).
Since 15376 is between 10000 and 16900, its square root must be between 100 and 130. All the given options (128, 134, 122, 124) are in or near this range, so checking them is necessary.
Also, look at the last digit of the number. 15376 ends in 6. The square of a number ending in 4 or 6 ends in 6 (\(4^2 = 16\), \(6^2 = 36\)). This helps narrow down possibilities if you know the last digit of the square root.
- 128 ends in 8 (\(8^2 = 64\), ends in 4).
- 134 ends in 4 (\(4^2 = 16\), ends in 6).
- 122 ends in 2 (\(2^2 = 4\), ends in 4).
- 124 ends in 4 (\(4^2 = 16\), ends in 6).
Both 124 and 134 end in a digit whose square ends in 6. Our calculation confirmed 124 is the correct one.
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Important Questions from Integers
Find the value of \(\sqrt{2025}\) .
How many times does the number 5 occur in the range of numbers from 1 to 100?
A. 21
B. 22
C. 20
D. 19
A prime number
A. is not a positive integer.
B. has no divisor at all.
C. has only 1 and itself as divisors.
D. has more than two divisors.
__________ are twin prime number.
A. (4, 9)
B. (2, 3)
C. (4, 6)
D. (3, 5)A factory produced 18,58,509 cassettes in the month of January, 7623 more cassettes in the of February and owing to short supply of electricity produced 25,838 less cassettes in March than in February. Find the total production in all?
A. 55,57,312
B. 59,83,245
C. 55,64,935
D. 56,08,988
