Radicals-> Exponential equations

In summary, radicals and exponential equations are two different ways of representing the same mathematical operation, with radicals using a root symbol (√) and exponential equations using an exponent. To solve a radical equation, you can use the property that taking the nth root of a number is equivalent to raising that number to the 1/n power. The index in a radical expression indicates which root is being taken, and some radical equations can have multiple solutions. In real life, radical equations are used in various fields such as engineering, physics, and finance to represent different concepts and calculations.
  • #1
rock4christ
34
0
how would I take the cube root of the square root of 2 as an exponential equation? the square root of 2 is 21/2 but I don't know what to do with the cube root.
 
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  • #2
The cubed root of x is x1/3. So, your expression for the cubed root of the square root of 2 is [tex](2^{\frac{1}{2}})^{\frac{1}{3}}[/tex]. Can you simplify this?
 
  • #3
well Id have to simplify it, because I am supposed to turn the new simplified exponent to a radical
 
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  • #4
Was that an answer to Cristo's question?? He asked do you know HOW to simplify it.
 
  • #5
oh, no i don't know how
 

1. What is the difference between radicals and exponential equations?

Radicals and exponential equations are two different ways of representing the same type of mathematical operation. Radicals use a root symbol (√) to indicate the inverse of an exponent, while exponential equations use an exponent to indicate repeated multiplication. For example, the radical √4 is equivalent to the exponential equation 41/2.

2. How do I solve a radical equation?

To solve a radical equation, you can use the property that taking the nth root of a number is equivalent to raising that number to the 1/n power. For example, to solve the equation √x = 4, you can rewrite it as x1/2 = 4 and then raise both sides to the 2nd power to get x = 16.

3. What is the meaning of the index in a radical expression?

The index in a radical expression indicates which root is being taken. For example, a square root has an index of 2 while a cube root has an index of 3. When no index is shown, it is assumed to be a square root.

4. Can radical equations have more than one solution?

Yes, some radical equations can have multiple solutions. This is because the same number can have multiple roots. For example, √4 has two solutions: 2 and -2. However, in some cases, a radical equation may only have one solution or no real solutions.

5. How are radical equations used in real life?

Radical equations are used in a variety of real-life applications, including engineering, physics, and finance. For example, in physics, the equation √E = mc2 is used to calculate the mass-energy equivalence in Einstein's famous theory of relativity. In finance, the compound interest formula A = P(1+r/n)nt uses radicals to represent continuous compounding over time.

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