What is the negative square root of 361
The Correct Answer and Explanation is:
The negative square root of 361 is –19.
Explanation:
To understand this, we begin with the concept of square roots. The square root of a number is a value that, when multiplied by itself, gives the original number. In symbols, ifx2=a,x^2 = a,x2=a,
thenx=aorx=−a.x = \sqrt{a} \quad \text{or} \quad x = -\sqrt{a}.x=aorx=−a.
In this case, the number is 361. We need to find the number which, when multiplied by itself, equals 361.
Let us test:19×19=361.19 \times 19 = 361.19×19=361.
This means that the positive square root of 361 is 19. However, since both positive and negative numbers can produce the same square when multiplied by themselves, we also have:(−19)×(−19)=361.(-19) \times (-19) = 361.(−19)×(−19)=361.
So, the square root of 361 actually has two values:361=±19.\sqrt{361} = \pm 19.361=±19.
The question specifically asks for the negative square root, so we focus only on the negative value:Negative square root of 361=−19.\text{Negative square root of 361} = -19.Negative square root of 361=−19.
Additional Insight:
It is important to understand that the square root symbol (√) usually refers to the principal (positive) square root by default. So when someone writes361,\sqrt{361},361,
it typically means 19. If the problem specifically asks for the negative square root, we include the minus sign explicitly in front of the square root symbol:−361=−19.-\sqrt{361} = -19.−361=−19.
This distinction is often emphasized in algebra and higher-level math to avoid confusion, especially when solving equations such asx2=361.x^2 = 361.x2=361.
In that case, the full set of solutions isx=±19.x = \pm 19.x=±19.
But if the question targets only the negative root, the answer is simply –19.
