9:{"metadata":[["$","title","0",{"children":"IPMAT Indore 2025 (SA) - The number of factors of 3^5 x 5^8 x 7^2 that are perfect squares is | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined A perfect square factor will have the form 3^a 5^b 7^c where each exponent must be even. This is because a perfect square is a number that can be expressed as n^2 for some inte>=r n.

For our number 3^5 5^8 7^2, we need to find all possib<= even exponents that don't exceed the original exponents: - For 3^5: The exponent a can be 0, 2, 4 (3 possibilities) - For 5^8: The exponent b can be 0, 2, 4, 6, 8 (5 possibilities) - For 7^2: The exponent c can be 0, 2 (2 possibilities)

Using the multiplication princip<=, the total number of perfect square factors is: 3 5 2 = 30

Therefore, the number of factors of 3^5 5^8 7^2 that are perfect squares is 30."}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"IPMAT Indore,SA,Number System,Factorisation"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"IPMAT Indore 2025 (SA) - The number of factors of 3^5 x 5^8 x 7^2 that are perfect squares is | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined A perfect square factor will have the form 3^a 5^b 7^c where each exponent must be even. This is because a perfect square is a number that can be expressed as n^2 for some inte>=r n.

Using the multiplication princip<=, the total number of perfect square factors is: 3 5 2 = 30

Therefore, the number of factors of 3^5 5^8 7^2 that are perfect squares is 30."}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/ipmat-jipmat-past-year-questions/ipmat-indore-2025/SA/14"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | IPMAT Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20IPMAT%20JIPMAT%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"IPMAT Indore 2025 (SA) - The number of factors of 3^5 x 5^8 x 7^2 that are perfect squares is | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined A perfect square factor will have the form 3^a 5^b 7^c where each exponent must be even. This is because a perfect square is a number that can be expressed as n^2 for some inte>=r n.

Using the multiplication princip<=, the total number of perfect square factors is: 3 5 2 = 30

Therefore, the number of factors of 3^5 5^8 7^2 that are perfect squares is 30."}],"$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20","$L21"],"error":null,"digest":"$undefined"}

IPMAT Indore 2025 (SA) PYQs

Keyboard Shortcuts