what is the square root of 168
The Correct Answer and Explanation is:
✅ Correct Answer:
The square root of 168 is approximately 12.9614813977.
📘 Explanation
The square root of a number is a value that, when multiplied by itself, gives the original number. So, the square root of 168 is the number which, when squared (multiplied by itself), equals 168.
In mathematical terms:168≈12.961\sqrt{168} \approx 12.961168≈12.961
To understand this better, let’s first consider perfect squares close to 168:
- 122=14412^2 = 144122=144
- 132=16913^2 = 169132=169
Since 168168168 lies between 144144144 and 169169169, we know that:12<168<1312 < \sqrt{168} < 1312<168<13
But because 168168168 is just one less than 169169169, its square root will be very close to 13, but slightly less.
We can find a more accurate value using long division or a calculator, which gives:168≈12.9614813977\sqrt{168} \approx 12.9614813977168≈12.9614813977
📐 Simplifying Square Root of 168
Sometimes we can simplify square roots by factoring out perfect squares:168=4×42168 = 4 \times 42168=4×42
Since 4 is a perfect square:168=4×42=4×42=242\sqrt{168} = \sqrt{4 \times 42} = \sqrt{4} \times \sqrt{42} = 2\sqrt{42}168=4×42=4×42=242
So, the square root of 168 in simplest radical form is:242\boxed{2\sqrt{42}}242
And in decimal form:242≈2×6.4807=12.96142\sqrt{42} \approx 2 \times 6.4807 = 12.9614242≈2×6.4807=12.9614
💡 Summary
- Square root of 168 is approximately 12.961.
- In simplest radical form, it is 2√42.
- It lies between 12 and 13.
- Square roots are used in geometry, physics, engineering, and many real-world applications where quantities grow quadratically.
