[MUSIC] escaped from radical prison adapted from a story by Mrs. Paxton. Two twin brothers were sent to radical prison for a crime they didn’t commit while in prison. They were broken down and worked very hard, but they stayed together. Finally, they decided to escape by digging under the prison wall. Only twins could attempt this escape together. The escape was too dangerous, and one of the twins died. The twin, who escaped wasn’t sure if he was happy because he escaped or sad because he lost his brother warning. When radical prison is empty, it magically disappears. It is never seen again. The radical sign is the checkmark symbol when there’s no number inside, it’s called a square root. When you’re taking the square root of a number. You’re looking for twins or square numbers in order to simplify it. Once you find twins one dies and one escapes, lets. Do some examples were gonna go ahead and start solving so? I’m going to show you how to simplify each square root. I’m gonna break each one down and look for twins, so I break down. 9 is really 3 times. 3 and 16 is 4 times 4 I now have twins One dies. One escapes one dies one escapes, So the square root of 9 over 16 is really 3/4 number two. I can break down Point 81 to be 0.9 times 0.9 Now I have twins. One dies one escape. So the positive or negative square root of 0.81 is positive or negative zero point, nine number. Three, the negative of the square root of 49 49 can be broken down into the twin seven times seven. I now have twins. One dies. One escapes. So the answer is negative. Seven number four. You cannot take the square root of a negative number. This is not possible! Hey, you cannot have a negative inside. You can have a negative on the outside, but not on the inside. That’s not possible Number Five, the square root of 50 okay. I can break 50 down and say 50 is the same as 5 times 10 No twins, let’s keep going. I can rewrite the 5 and 10 I know is 5 times 2 Hey, now I have twins. So one dies one escapes. This two does not have a twin, so it stays inside the radical or the square root. Five escaped square root 2 The square root of 50 is also 5 times, the square root of 2 number 6 square root of 72 I know I can multiply 9 times 8 to make 72 Let’s keep going 9 is also 3 times 3 and 8 is 4 times 2 hmm? I have twins, but if I break 4 down, they’ll be more, so I’m gonna keep going. I rewrite by 3 times 3 or it turns into 2 times 2 and bring down that other two. Okay, my threes are twins. One dies one escapes. I have triplets so one dies. One escapes and this 2 does not have a twin to go is so it stays inside the radical everything that escapes gets multiplied together. So 3 times 2 is 6 A six escaped and the two is left inside the square root of 72 is the same as 6 times, the square root of 2 number 7 square root of 18 I know I can multiply 6 times 3 to make 18 I don’t have any twins. So if I break sticks apart, I get 2 times 3 for 6 Bring down the other 3 now. I have twins one. Sighs one escapes. The two stays inside, so a three escaped and a two is left inside the radical. The square root of 18 is also three times the square root of 2 All right, number eight. The square root of 48 48 can be broken down a few ways. I’m going to do six times eight. So I know six is really two times. Three and eight is four times two. I don’t have, I know if I break that four down. I get more twins, so I’m gonna keep going so two times. Three four turns into two times to bring down the other two all right now! I’ve got twins. I’ve got this too in this too, so one dies. One escapes, here’s another set. One dies. One escapes. Everything that escapes multiplies together. Two times two is four four escaped and this three nothing happened. It’s left inside. Therefore, the square root of 48 is the same as four times the square root of three. All right, we’re gonna solve each equation. The inverse operation or the opposite of something squared is two square root it so we get rid of squared. We square root both sides square root square root, So a squared is really a times. A 289 can also be known as 17 times 17 now. I’ve got twins. One dies, one escapes, one dies one escapes, So I get a equals positive or negative 17 anytime you solve an equation, your answers need positive or negative, so we’re gonna say answers to X squared equations, meet the plus or minus side. They don’t know if they’re happy or if they’re sad. All right, number 10 N Squared equals 0.09 take the square root of both sides because that’s the inverse operation. N Squared can be M times. M 0.09 can be zero point three times zero point three. Now we’ve got twins. One dies. One escapes positive or negative One dies. One escapes the last one. I’m going to take the square root of both sides, So Y squared can be Y time’s y for over 25 I keep it in. Fraction form 4 is 2 times 2 25 is 5 times 5 I’ve got twins. One dies one escape. So it’s y equals positive or negative. Two one dies, one escapes. Five one dies, one escapes [Music].