Evaluate √3√12√40√48

sqtot = 4

We have a product of 4 square root terms

The product of square roots is equal to the square root of the products

√3√12√40√48 = √3*12*40*48

√3√12√40√48 = √69120

Simplify √69120.

Checking square roots, we see that 262

Our answer in decimal format is between 262 and 263

Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

√69120 = √1√69120

√69120 = √2√34560

√69120 = √3√23040

√69120 = √4√17280

√69120 = √5√13824

√69120 = √6√11520

√69120 = √8√8640

√69120 = √9√7680

√69120 = √10√6912

√69120 = √12√5760

√69120 = √15√4608

√69120 = √16√4320

√69120 = √18√3840

√69120 = √20√3456

√69120 = √24√2880

√69120 = √27√2560

√69120 = √30√2304

√69120 = √32√2160

√69120 = √36√1920

√69120 = √40√1728

√69120 = √45√1536

√69120 = √48√1440

√69120 = √54√1280

√69120 = √60√1152

√69120 = √64√1080

√69120 = √72√960

√69120 = √80√864

√69120 = √90√768

√69120 = √96√720

√69120 = √108√640

√69120 = √120√576

√69120 = √128√540

√69120 = √135√512

√69120 = √144√480

√69120 = √160√432

√69120 = √180√384

√69120 = √192√360

√69120 = √216√320

√69120 = √240√288

√69120 = √256√270

From that list, the highest factor that has an integer square root is 2304.

Therefore, we use the product combo √69120 = √2304√30

Evaluating square roots, we see that √2304 = 48

√69120 =

48√30