Video: Solving Simple Radical Equations

Solve √(𝑥 + 4) + 2 = 7.

01:25

Video Transcript

Solve the root of 𝑥 plus four plus two equals seven.

And we’re gonna start to solve this problem. The first thing to look at is the fact that this plus two is actually outside of the root. Okay, this is one of the key things to actually take note of because it makes a difference when we’re actually doing the next steps of solving this equation.

The first stage in solving the equation is to actually subtract two from each side. So we’re gonna be left with root 𝑥 plus four is equal to five because seven minus two is equal to five. And now, because we actually have the root of 𝑥 plus four is equal to five, what we want to do is actually square both sides so that we actually have an 𝑥-value rather than root 𝑥-value.

So we’re gonna get 𝑥 plus four first because if you square a square root, you just get what’s left within the root sign. So the square of the root of 𝑥 plus four is just 𝑥 plus four. And then this is equal to 25 because five squared is five multiplied by five which is 25. And then finally, what we do is we actually subtract four from each side. So we’re left with 𝑥 is equal to 21.

So therefore, we can say that root 𝑥 plus four plus two equals seven, fully solved, gives us 𝑥 is equal to 21.

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