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[Junior high school mathematics] The product root is equal to the multiplication of the product factor root, and the quotient root is equal to the dividend root and the divisor root. How to prove it?
Hello, the certificate is as follows:

1. Prove that the product root is equal to the product of the product factor root;

Let the product be ab and the factors be A and B respectively. Then the square root of the product is (AB) 1/2, which is exactly equal to A 1/2× B 1/2, that is, it is equal to the square root multiplication of the product factor. The proposition is proved;

2. Prove that the quotient root is equal to the dividend. Eradicate by divisor root:

Let the quotient be A/B, and the dividend and divisor are a and b respectively. Then the root of the quotient is equal to (a/b) 1/2, which is exactly equal to a 1/2/b 1/2, that is, it is equal to the root of the divisor. The proposition is proved.

I hope I can help you.