Between which two consecutive integers is -√26? Do not use a calculator.

Verified step by step guidance

1. Recognize that $-\sqrt{26}$ is the negative square root of 26.
2. Estimate the square root of 26 by identifying perfect squares around 26. Note that $5^2=25$ and $6^2=36$.
3. Since $25<26<36$, it follows that $5<\sqrt{26}<6$.
4. Apply the negative sign to the inequality: $-6<-\sqrt{26}<-5$.
5. Conclude that $-\sqrt{26}$ is between the consecutive integers $-6$ and $-5$.

Key Concepts

Square Roots

The square root of a number 'x' is a value 'y' such that y² = x. For negative numbers, the square root is not defined in the set of real numbers. In this case, -√26 represents the negative square root of 26, which is a real number and will be less than zero.

Estimating Square Roots

To estimate the square root of a non-perfect square, we can find the two perfect squares it lies between. For √26, we know that 5² = 25 and 6² = 36, so √26 is between 5 and 6. This helps us determine the range for -√26, which will be between -6 and -5.

Consecutive Integers

Consecutive integers are numbers that follow one another in order without any gaps. For example, -6 and -5 are consecutive integers. Understanding this concept is crucial for identifying the two integers between which -√26 lies, as it requires recognizing the integer values immediately surrounding the estimated square root.