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5 sty 2023 · Again, we call this an extraneous solution as we did when we solved rational equations. In the next example, we will see how to solve a radical equation. Our strategy is based on raising a radical with index n n to the nth n t h power. This will eliminate the radical. For a ≥ 0, (a−−√n)n = a a ≥ 0, (a n) n = a.
A radical equation is any equation that contains one or more radicals with a variable in the radicand. Following are some examples of radical equations, all of which will be solved in this section: √x − 1 = 5 √2x − 5 + 4 = x 3√x2 + 4 − 2 = 0.
Rewrite the expressions with similar fractional exponents in radical form. Example 1: Make the indices of √3 and ∛2 similar. Solution: 1. Write the given radicals as expressions with fractional exponents. You will notice that the fractional exponents are dissimilar fractions.
What is Radical? The radical of a number is the same as the root of a number. The root can be a square root, cube root, or in general, n th root. Thus, any number or expression that uses a root is known as a radical. The term radical is derived from the Latin word Radix which means root.
The above relations enable us to express radicals as fractional exponents and fractional exponents as radicals. EXAMPLES 1. root(5,3)=3^(1/5) 2. root(3,2^2)=2^(2/3) 3. root(x+3)=(x+3)^(1/2) 4. x^(4/5)=root(5,x^4) 5. 3x^(3/4)=3root(4,x^3) 6.
A common method for solving radical equations is to raise both sides of an equation to whatever power will eliminate the radical sign from the equation. But be careful: when both sides of an equation are raised to an even power, the possibility exists that extraneous solutions will be introduced.
