nth roots
Master nth roots in Grade 10 math. Radical expressions of the form are called nth roots. In this form n is the index and a is the radic. Practice with Saxon Algebra 2 examples.
Key Concepts
Radical expressions of the form $\sqrt[n]{a}$ are called nth roots. In this form n is the index and a is the radicand. $\sqrt[n]{a} = b$ if $b^n = a$. When nth roots have an odd index, there is only one real root. When they have an even index and a positive radicand, there are two real roots.
The cube root of 27: $\sqrt[3]{27} = 3$ because $3^3 = 27$. The index is odd, so there is one real root. The fourth root of 81: $\sqrt[4]{81} = \pm 3$ because both $3^4 = 81$ and $( 3)^4 = 81$. The index is even. The cube root of 8: $\sqrt[3]{ 8} = 2$ because $( 2)^3 = 8$. The odd index allows a negative radicand.
The 'nth root' is like asking, 'What number, when multiplied by itself n times, gives me the number inside the radical?' The little 'n' is your guide. Be careful! An even index on a negative number is a no go in the real number world because a real number multiplied by itself an even number of times can’t be negative.
Common Questions
What is nth roots?
Radical expressions of the form are called nth roots. In this form n is the index and a is the radicand. if . When nth roots have an odd index, there is only one real root. When they have an even index and a positive radicand, there are two real roots. Think of finding an nth root like solving a...
How do you apply nth roots in practice?
The cube root of 27: because . The index is odd, so there is one real root. The fourth root of 81: because both and . The index is even. The cube root of -8: because . The odd index allows a negative radicand.
Why is nth roots important for Grade 10 students?
Think of a cube root like finding the side length of a cube when you know its volume. For , we're just asking: what number multiplied by itself three times gives you -64? The cool thing is that unlike square roots, you can find the root of a negative number when the index (the little number like...