How do you simplify 3 times the square root 13?
The correct answer and explanation is:
To simplify the expression 3×133 \times \sqrt{13}, you need to first understand that this is a product of a constant (3) and a square root. Since 13 is a prime number, it does not have any square factors other than 1, so the square root cannot be simplified further.
The expression 3×133 \times \sqrt{13} is already in its simplest form. This means there is no way to break it down into a more simplified square root or a whole number.
Here’s why:
- Square Roots and Prime Numbers: The square root of a number is the value that, when multiplied by itself, equals that number. In this case, 13\sqrt{13} is the value that, when squared, gives 13. Since 13 is prime, it doesn’t have any factors other than 1 and 13 itself. This means 13\sqrt{13} is already in its simplest radical form.
- Multiplying by a Constant: The constant 3 in the expression 3×133 \times \sqrt{13} is a simple multiplier. It doesn’t affect the radical, so the expression cannot be simplified any further.
- Rationalizing the Expression: In some cases, expressions involving square roots may be simplified by rationalizing the denominator (if there is one). However, in this case, the expression doesn’t involve a fraction, so there’s no need to rationalize anything.
Thus, the expression remains 3×133 \times \sqrt{13} and it is already simplified. In decimal form, this expression can be approximated as: 3×13≈3×3.60555=10.816653 \times \sqrt{13} \approx 3 \times 3.60555 = 10.81665
However, unless the problem specifically asks for a decimal answer, it is generally best to leave the expression in its simplest radical form, which in this case is 3×133 \times \sqrt{13}.